Abstract
We investigate the properties of dark matter (DM) distribution in spiral galaxy U5750, employing the well known and widely used phenomenological density profiles such as pseudo-isothermal, Burkert, Navarro-Frenk-White, Einasto, Moore and exponential sphere. For simplicity we assume that DM distribution is spherically symmetric without accounting for the complex internal structure of the galaxy. We fit the rotation curve observational data of galaxy U5750 for each profile. We infer the model free parameters and estimate the total DM mass, and compare them with those reported in the literature. To discriminate the best fit profile among the considered ones, we make use of the Bayesian Information Criterion (BIC). On the basis of the performed statistical analysis, we provide physical interpretations for choosing certain profiles. In addition, by assuming that DM possesses non-zero pressure, we solve the Newtonian hydrostatic equilibrium equation and construct the pressure profiles as a functionof the radial coordinate for each above mentioned profile. Combining the density profiles with the pressure profiles we obtain equations of state for the DM in the considered galaxy. Further, we calculate the speed of soundin the DM medium and show that it behaves not unequivocally for the adopted profiles, though it decreaseswith an increasing DM density. Finally, we calculate the refracting index and discuss about astrophysical implications of the obtained results.